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    "# 高中物理力学公式大全\n",
    "\n",
    "## 1. 运动学\n",
    "\n",
    "### 匀速直线运动\n",
    "$$ v = \\frac{s}{t} $$\n",
    "$$ s = vt $$\n",
    "\n",
    "### 匀变速直线运动\n",
    "#### 基本公式\n",
    "$$ v = v_0 + at $$\n",
    "$$ s = v_0t + \\frac{1}{2}at^2 $$\n",
    "$$ v^2 - v_0^2 = 2as $$\n",
    "\n",
    "#### 平均速度\n",
    "$$ \\bar{v} = \\frac{v_0 + v}{2} = \\frac{s}{t} $$\n",
    "\n",
    "#### 中间时刻速度\n",
    "$$ v_{\\frac{t}{2}} = \\bar{v} = \\frac{v_0 + v}{2} $$\n",
    "\n",
    "#### 重要推论\n",
    "$$ \\Delta s = aT^2 \\quad ({相邻相等时间位移差}) $$\n",
    "\n",
    "### 自由落体运动\n",
    "$$ v = gt $$\n",
    "$$ h = \\frac{1}{2}gt^2 $$\n",
    "$$ v^2 = 2gh $$\n",
    "\n",
    "### 竖直上抛运动\n",
    "$$ v = v_0 - gt $$\n",
    "$$ h = v_0t - \\frac{1}{2}gt^2 $$\n",
    "$$ v^2 - v_0^2 = -2gh $$\n",
    "\n",
    "## 2. 曲线运动\n",
    "\n",
    "### 平抛运动\n",
    "#### 水平方向\n",
    "$$ v_x = v_0 $$\n",
    "$$ x = v_0t $$\n",
    "\n",
    "#### 竖直方向\n",
    "$$ v_y = gt $$\n",
    "$$ y = \\frac{1}{2}gt^2 $$\n",
    "\n",
    "#### 合运动\n",
    "$$ v = \\sqrt{v_x^2 + v_y^2} $$\n",
    "$$ \\tan\\theta = \\frac{v_y}{v_x} = \\frac{gt}{v_0} $$\n",
    "\n",
    "### 圆周运动\n",
    "#### 线速度与角速度\n",
    "$$ v = \\omega r $$\n",
    "$$ \\omega = \\frac{2\\pi}{T} = 2\\pi f $$\n",
    "\n",
    "#### 向心加速度\n",
    "$$ a = \\frac{v^2}{r} = \\omega^2r = \\frac{4\\pi^2r}{T^2} $$\n",
    "\n",
    "#### 向心力\n",
    "$$ F = m\\frac{v^2}{r} = m\\omega^2r $$\n",
    "\n",
    "## 3. 动力学\n",
    "\n",
    "### 牛顿第二定律\n",
    "$$ F = ma $$\n",
    "\n",
    "### 牛顿第三定律\n",
    "$$ F_{12} = -F_{21} $$\n",
    "\n",
    "### 万有引力定律\n",
    "$$ F = G\\frac{m_1m_2}{r^2} $$\n",
    "\n",
    "### 重力\n",
    "$$ G = mg $$\n",
    "$$ g = \\frac{GM}{R^2} $$\n",
    "\n",
    "## 4. 功和能\n",
    "\n",
    "### 功\n",
    "$$ W = Fs\\cos\\theta $$\n",
    "\n",
    "### 功率\n",
    "$$ P = \\frac{W}{t} = Fv\\cos\\theta $$\n",
    "\n",
    "### 动能\n",
    "$$ E_k = \\frac{1}{2}mv^2 $$\n",
    "\n",
    "### 动能定理\n",
    "$$ W = \\Delta E_k = \\frac{1}{2}mv_2^2 - \\frac{1}{2}mv_1^2 $$\n",
    "\n",
    "### 重力势能\n",
    "$$ E_p = mgh $$\n",
    "\n",
    "### 机械能守恒\n",
    "$$ E_{k1} + E_{p1} = E_{k2} + E_{p2} $$\n",
    "\n",
    "### 弹性势能\n",
    "$$ E_p = \\frac{1}{2}kx^2 $$\n",
    "\n",
    "## 5. 动量\n",
    "\n",
    "### 动量\n",
    "$$ p = mv $$\n",
    "\n",
    "### 冲量\n",
    "$$ I = Ft $$\n",
    "\n",
    "### 动量定理\n",
    "$$ Ft = mv_2 - mv_1 $$\n",
    "\n",
    "### 动量守恒\n",
    "$$ m_1v_1 + m_2v_2 = m_1v_1' + m_2v_2' $$\n",
    "\n",
    "## 6. 静力学\n",
    "\n",
    "### 力的合成与分解\n",
    "$$ F = \\sqrt{F_1^2 + F_2^2 + 2F_1F_2\\cos\\theta} $$\n",
    "$$ \\tan\\varphi = \\frac{F_2\\sin\\theta}{F_1 + F_2\\cos\\theta} $$\n",
    "\n",
    "### 力矩\n",
    "$$ M = FL $$\n",
    "\n",
    "### 平衡条件\n",
    "$$ \\sum F = 0 $$\n",
    "$$ \\sum M = 0 $$\n",
    "\n",
    "## 7. 振动和波\n",
    "\n",
    "### 简谐运动\n",
    "$$ F = -kx $$\n",
    "$$ a = -\\frac{k}{m}x $$\n",
    "\n",
    "### 单摆周期\n",
    "$$ T = 2\\pi\\sqrt{\\frac{L}{g}} $$\n",
    "\n",
    "### 弹簧振子周期\n",
    "$$ T = 2\\pi\\sqrt{\\frac{m}{k}} $$\n",
    "\n",
    "### 波速公式\n",
    "$$ v = \\lambda f = \\frac{\\lambda}{T} $$\n",
    "\n",
    "## 8. 常用常数\n",
    "\n",
    "| 物理量 | 符号 | 数值 |\n",
    "|--------|------|------|\n",
    "| 重力加速度 | $g$ | $9.8 {m/s}^2$ |\n",
    "| 万有引力常量 | $G$ | $6.67 \\times 10^{-11} {N·m}^2/{kg}^2$ |\n",
    "\n",
    "## 💡 重要概念\n",
    "\n",
    "1. **惯性参考系**：牛顿定律成立的参考系\n",
    "2. **超重与失重**：$N = mg + ma$ 或 $N = mg - ma$\n",
    "3. **完全弹性碰撞**：动量守恒 + 动能守恒\n",
    "4. **非弹性碰撞**：动量守恒，动能不守恒\n",
    "\n",
    "## 📝 解题技巧\n",
    "\n",
    "1. 明确研究对象，进行受力分析\n",
    "2. 建立合适的坐标系\n",
    "3. 应用牛顿第二定律列方程\n",
    "4. 注意能量守恒和动量守恒的条件\n",
    "5. 检查结果的合理性和单位\n",
    "\n",
    "## 9. 重要推论\n",
    "\n",
    "### 连接体问题\n",
    "$$ a = \\frac{F}{m_1 + m_2} $$\n",
    "\n",
    "### 斜面问题\n",
    "$$ a = g\\sin\\theta \\quad ({光滑斜面}) $$\n",
    "$$ a = g(\\sin\\theta - \\mu\\cos\\theta) \\quad ({粗糙斜面}) $$\n",
    "\n",
    "### 弹簧问题\n",
    "$$ F = kx $$\n",
    "$$ T = 2\\pi\\sqrt{\\frac{m}{k}} $$\n",
    "\n",
    "> 掌握这些公式和理解其物理意义是解决力学问题的关键。"
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